Article pubs.acs.org/IECR
Artificial Neural Networks and the Melting Temperature of Ionic Liquids José O. Valderrama,*,†,‡ Claudio A. Faúndez,§ and Vilma J. Vicencio∥ †
Faculty of Engineering, Department of Mechanical Engineering, and ∥Faculty of Sciences, Department of Chemical Engineering, University of La Serena, Casilla 554, La Serena, Chile ‡ Center for Technological Information, c/Monseñor Subercaseaux 667, La Serena, Chile § Faculty of Physical and Mathematical Sciences, University of Concepción, P.O. Box 160-C, Concepción, Chile S Supporting Information *
ABSTRACT: The use of artificial neural networks (ANNs) for the correlation and prediction of the melting temperature of ionic liquids (ILs) is analyzed in this paper. Several network architectures and two sets of data were analyzed and the results compared with others from the literature. The independent variables (those that could have an influence on the melting temperature) considered for training the ANNs were the groups forming the molecules, mass of the cation, mass of the anion, and mass connectivity index. These properties are easily available or are calculated and are provided as Supporting Information. As a measure of the accuracy of the method, the average deviation and average absolute deviation are evaluated. The results of this work and others from the literature indicate that appropriate selection of data and a good combination of architecture and variables can lead to an acceptable correlation of data, but accurate prediction is not yet possible. The lack of a clear definition of the melting temperature and the lack of knowledge on what are the properties that most affect melting are the main causes of the present incapability of accurately predicting the melting temperature of any IL.
1. INTRODUCTION From an industrial point of view, a fundamental understanding of the chemical, physical, and thermodynamic properties of ionic liquids (ILs) should be known before their industrial application. For instance, knowledge of some basic properties is useful in the area of fluid property estimation, thermodynamic property calculations, and phase equilibrium, among others. Properties such as the melting temperature, density, and viscosity are related to mechanical and engineering processes, so ways to determine them either experimentally or predicted in semitheoretical form are needed.1 The melting temperature is a fundamental physicochemical property of a molecule that is controlled by both singlemolecule properties and intermolecular interactions because packing in the solid state. The melting process of ILs is complex and still not well understood. However, we know a few facts: (i) the same sample of ILs may have both a glass transition temperature and a melting temperature;2 (ii) the melting process of ILs is governed by van der Waals forces and electrostatic interaction forces, and the two forces play different roles for different kinds of ILs;3 (iii) the complex influence of energy and entropy factors makes prediction of the melting temperatures of ILs a difficult task.4,5 In a recent paper, some of the methods presented in the literature during the past few years to estimate the melting temperature of ILs and the alleged accuracy of the methods presented by several authors were discussed.6 One of the methods mentioned was artificial neural networks (ANNs), but the paper did not give much detail about the limitations of ANNs for this particular application of correlating the melting temperature of ILs. In fact, the ANN method has been seen by © 2014 American Chemical Society
many researchers as a general and appropriate correlating and predicting tool for any situation, with almost no restrictions.6 Taskinen and Yliruusi7 have reviewed the several properties that have been analyzed in the literature using ANNs. The melting temperature was not discussed by these authors. However, some works on the application of ANNs to correlate the melting temperatures of organic substances and also of ILs have been presented in the literature.8,9 In this paper, the performance of several configurations of ANNs in correlating and predicting the melting temperature of ILs is analyzed. The application does not give any special information for a better understanding of the way in which the melting temperature of ILs behaves, but it provides new information about the limitations of ANNs for correlating the melting temperature of ILs.
2. ANNs ANNs are a computational tool inspired by the behavior of natural neurons.10 Units resembling neurons are organized in a defined structure form by layering of a certain arbitrary but defined number of neurons. The input layer receives data of a given property and set of variables that are supposedly related to the dependent main variable. The input and output variables are related, giving them certain weight, and are shifted by a bias factor specific to each neuron. The network finds a relationship between the variables in a loop of calculations and using some Received: Revised: Accepted: Published: 10504
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the problem of predicting the melting temperature of ILs in an acceptable way. This view agrees with that of other authors (“But, even if a pure substance was synthesized, and the melting temperature was unequivocally determined, there might be a multitude of unfavorable factors”) for developing a model for the prediction of the melting temperature of ILs.13 Figure 1 presents a simple diagram of an ANN method that we have used for correlating and predicting several properties
optimization routine. Then it stores the values of the weights and biases that give the lowest error between calculated and experimental data of the dependent variable. These values define the ANN model. ANNs have several unique characteristics and advantages for applications such as prediction of the physicochemical properties of the substances. One of these features is their adaptive nature. The process of learning by training is used instead of the conventional “programming” commonly used in modeling. This feature makes ANNs very attractive for applications where the relationship between variables is not well-known but data are readily available for training. Table 1 shows some advantages and disadvantages of ANNs. The aspects mentioned in Table 1 indicate that, although Table 1. Some Advantages and Disadvantages of ANNs Advantages 1 2 3 4 5 6
A neural network can perform tasks that a linear program cannot. If an element of the ANN fails, it can continue without any problem. A neural network learns and does not need to be reprogrammed. It can be implemented in any application, and it is easy to set up. Models do not have to be specified in advance. They are able to fit complex nonlinear models. Disadvantages
1 2 3 4 5 6
The neural network needs training to operate. The best architecture must be known or determined by trial and error. They require a large amount of accurate data. They need to know several variables well related to the target variable. Local minima generalization/overfitting are difficult to interpret. They can suffer from overfitting and overtraining.
Figure 1. Flow diagram of the ANN method showing the connections between the different program and data files.
of ILs including the melting temperature, using Matlab. Connections between the different files created for training and testing can be observed in the figure. The file w_tm is the weight matrix that defines the ANN model. The application of ANNs also requires first collection of accurate enough data for the property of interest, the melting temperature, the first block in the diagram of Figure 1. The Matlab code corresponding to the diagram of Figure 1 is provided as Supporting Information.
ANNs represent useful mathematical tools, their applications must be taken with care. In particular, the requirement of a large amount of accurate data (which depends on the complexity of the problem) and the knowledge of which are the most appropriate variables have more influence on the target variable. Considering the many applications found in the literature, the low accuracy found in many cases, and mainly the lack of knowledge about what is mathematically behind the ANN algorithm, it seems that there is a generalized assumption that ANN can be used for correlating and predicting the properties if just enough data are available for the variable of interest (for instance, the melting temperature). This general belief is simply not true.6 Livingstone and co-workers11 wrote, “data modeling with neural networks is certainly not an answer to the maiden’s prayer, but neural networks do offer a number of advantages over some of the more traditional methods of data modeling and should be viewed as a useful adjunct to these techniques”. To take advantage of the good characteristics and properties of ANNs, one must know what is really happening during training and testing. For the case of interest here, that is, correlating and predicting the melting temperature of ILs, there is not enough information (for instance, other properties of ILs) to find an appropriate relationship between Tm and other variables. Also, data reported in the literature that are used to train the ANNs are of unknown accuracy, and in many cases, very different values are reported for the same IL.12 The true value of Tm (if there is any) is unknown. This is one of the reasons for the little progress done on this area. However, even if accurate data were available, with the present state of knowledge, ANNs cannot give a clear answer to
3. LITERATURE DATA OF Tm FOR ILs There are some databases, handbooks, and compilations of data for the melting temperature of ILs.14−16 The most complete compilation is that of Zhang et al.,16 which includes 1103 data of the melting temperature for 953 ILs. New data frequently appear in journals and monographs. However, several of the reported values of Tm for the same ILs may show great differences. It is known that the thermal behavior of ILs is relatively complex, a fact that may explain the great differences in Tm values found in the literature. Valderrama and Rojas12 discussed the deviations between the experimental melting temperature data published by different authors for many ILs. They showed that differences in the values of the melting temperature for the same ILs can be as high as 90 K. This is a worrisome fact because in ANN modeling inaccurate data may lead to the network not being able to find a reasonable relationship between the variables. The network could also memorize, giving excellent results during learning but having poor predicting capabilities.6 The study presented in this paper considers two main studies: (1) several architectures with 667 data points of the melting temperature of different types of ILs (567 data for training and 100 data for testing); (2) several architectures with 10505
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297 data points of the melting temperature of imidazolium-type ILs only (270 data for training and 27 data for testing). In both studies, the independent variables are the groups forming the molecules, mass of the cation, mass of the anion, and mass connectivity index. All of these data are provided as Supporting Information.
Table 3. Groups Gi Considered as Independent Variables in ANN Models for Study 2 (297 Data)
4. APPLICATIONS OF ANN MODELS A series of requirements must be fulfilled for an ANN model to be capable of correlating data: number of data, type and number of independent variables associated with the dependent variable (the property of interest), and the network architecture. In other applications and in this paper, we have combined group contributions with ANNs, plus other independent variables that are easily available, to correlate and predict the melting temperature of ILs. ILs are formed by ions, a well-differentiated anion and a welldifferentiated cation. Also, chemical groups forming the molecules can be identified, although such groups are more or less arbitrary. The sizes of the cation and anion and the types of groups forming the molecule are of importance in defining some properties of ILs, such as the melting temperature.2 Additionally, a structural parameter that involves the size and type of connections known as the mass connectivity index is useful for correlation purposes.17 Among the several independent variables that we have successfully used in ANN studies with ILs are the mass of the cation, mass of the anion, mass connectivity index,17 and groups forming the molecule (M+, M−, λ, Gi).18,19 In this work, two independent studies are presented, and in each study, the groups are defined in a different form, as shown in Table 2 for study 1 and in Table 3 for study 2. The information Table 2. Groups Gi Considered as Independent Variables in ANN Models for Study 1 (667 Data) no.
group
no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
−CH3 −CH2− >CH− >C< CH2 CH− (−)CH (−)C− −OH −O− >CO −COOH −COO− HCOO− O(ao) −NH2 −NH− >N− N−
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
no.
group
no.
group
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
−CH3 −CH2− >CH− >C< CH2 CH− CH C− −OH −O− >CO >CS −COOH −COO− −NH− >N− −CN −NO2 NO3 CF2 CF3 −F −Cl −Br −I ClO4 −P PF3
29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
PF6 −B BF4 BF3 −S− SF5 −SO2 SO3 SO4 C3H4N2 C3H3N2 C3H2N2 C3HN2 C3N2 C5H5N C6H5 C6H4 C6H3 C6 C5H4 AlCl4 SbF6 NbF6 AsF6 Si− Cr− Fe−
To develop an accurate model to predict the melting temperature of ILs in the form presented in this work, the following files were written: (a) an Excel file containing the independent variables: mass of the cation, mass of the anion, mass connectivity index, and the groups forming the molecule (M+, M−, λ, Gi); (b) an Excel file containing the dependent variable: melting temperature (Tm); (c) a Matlab code for the ANN that consists of two parts: (i) a training section and (ii) a prediction section. In the training section, the program reads the input data (two Excel files: variables_tm_training and tm_for_training), defines the architecture, trains the defined network, generates the weight and bias matrices, and stores these data for prediction. The correlated data are stored in an Excel file named tm_correlated. In the prediction section, the program reads the weight and bias matrices and an Excel file containing the variables for which the melting temperature needs to be predicted (variables_tm_prediction) and stores the results in an output Excel file (tm_predicted). Table 5 gives details about the required files and their function. All of these Excel files are provided as Supporting Information, so any reader can run the program, get our results, and use the model for other applications. The usual architecture normally used for these types of applications considers a back-propagation feed-forward neural network containing three or four layers: the input layer, one or two hidden layers, and the output layer.10 According to other studies, four-layer architectures with 5−25 neurons in the inner layers are appropriate for correlating the properties of fluids. The accuracy of the model was checked by determining the
group −CN −NO2 −F −Cl −Br −I −P −B −S− −SO2 −NH3 Si− (in rings) −CH2− CH− C< −NH− >N− N−
provided to the network is the number of times that a group appears in the molecule (frequency). In some molecules, one group may appear several times and some other groups may not appear. Table 4 gives a sample of data needed for the proposed ANNs and shows how the different groups must be defined for each IL to be accepted as an input variable by the ANN program. 10506
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10507
0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
cation formula
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
formula [C1im] [C1im] [C1im] [C1im] [C1im] [C1im] [C1im] [C1im] [Dmim] [C1mim] [Dmim] [C1im] [C1mim] [Me2NO2im] [Me2NO2im] [C1mim] [Bemim] [Bemim] [C2im] [M2,4,5im] G31 G32 G33
cnion name
1-methylimidazolium hexafluorophosphate C4H7N2F6P 1-methylimidazolium perchlorate C4H7N2ClO4 1-methylimidazolium tetrafluoroborate C4H7N2BF4 1-methylimidazolium bromide C4H7N2Br 1-methylimidazolium nitrate C4H7N3O3 1-methylimidazolium chloride C4H7N2Cl 1-methylimidazolium trifluoromethanesulfonate C5H7N2F3SO3 1-methylimidazolium trifluoroacetate C6H7N2F3O2 1,2-dimethylimidazolium hexafluorophosphate C5H9N2F6P 1,3-dimethylimidazolium tetrafluoroborate C5H9N2BF4 1,2-dimethylimidazolium nitrate C5H9N3O3 1-methylimidazolium acetate C6H10N2O2 1,3-dimethylimidazolium trifluoromethyltrifluoroborate C6H9N2F6B 1,3-dimethyl-5-nitroimidazolium perchlorate C5H8N3O6Cl 1,3-dimethyl-5-nitroimidazolium nitrate C5H8N4O5 1,3-dimethylimidazolium trifluoroacetate C7H9N2F3O2 1-benzyl-3-methylimidazolium hexafluorophosphate C12H13N2F6P 1-benzyl-3-methylimidazolium bromide C11H13N2Br 1-ethylimidazolium bromide C5H9N2Br 2,4,5-trimethylimidazolium chloride C6H11N2Cl G18 G19 G20 G21 G22 G23 G24 G25 G26 G27 G28 G29 G30
cation name
Table 4. Sample of Data Needed for the Proposed ANNs
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[PF6] [ClO4] [BF4] [Br] [NO3] [Cl] [TfO] [TA] [PF6] [BF4] [NO3] [Ac] [CF3BF3] [ClO4] [NO3] [ta] [PF6] [Br] [Br] [Cl] G34 G35
anion formula Mcation
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0
389.15 83114 430.15 83114 325.55 83114 314.15 83114 343.15 83114 345.15 83114 357.15 83114 324.15 83114 388.15 97141 376.55 97141 357.15 97141 250.15 83114 288.15 97141 445.15 142139 436.15 142139 325.15 97141 403.15 173239 399.15 173239 333.15 97141 467.15 111168 G36 G37 G38
Tm
λ
0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
144962 0.0826 99448 0.0868 86803 0.0885 79904 0.0896 62007 0.0933 35452 0.1032 149071 0.1165 113016 0.1353 144962 0.1462 86803 0.1522 62007 0.1570 59046 0.1768 136809 0.1849 9945 0.1879 62007 0.1944 113016 0.1991 144962 0.2093 79904 0.2163 79904 0.2296 35452 0.2317 G39 G40 G41
Manion
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 3 G42
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
G44
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G45
G3 G4 G5
G43
G1 G2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G47
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G48
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G49
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G52
0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G53
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G54
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G55
G6 G7 G8 G9 G10 G11 G12 G13 G14 G15 G16 G17
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Table 5. Description of the Files Given as Supporting Information To Correlate and Predict the Melting Temperatures of Other ILs file
no. 1
tm_training.m
2
tm_prediction.m
3
w_tm
4
variables_tm_training.xls
5
tm_for_training.xls
6
tm_correlated.xls
7
variables_tm_prediction.xls
8
tm_predicted.xls
description
details
Matlab code for training the net with melting temperature data Matlab code to predict the melting temperature of ILs using the trained ANN stores the ANN model with all of the parameters obtained during training contains the mass of the cation, mass of the anion, mass connectivity index, and groups contains the values of the melting temperature to be used in training of the network contains the values of the melting temperature determined by the network during training contains the required information for predicting the melting temperature for the compounds stores the predicted data for further study and analysis, if desired
reads the melting temperature data and the independent variables for training and contains the architecture of the ANN reads the independent variables for predicting the melting temperature for other ILs and other temperatures contains the weight matrix, bias array, and other files that define the ANN model for study 1, there were 37 groups, and for study 2, there were 55 groups
relative, absolute, and maximum deviations between calculated values of the melting temperature after training and data from the literature. Our group has been working for several years on applications of ANNs to property estimation, and it seems that good data selection, good classification of data (types of ILs), a reasonable amount of data, and appropriate selection of the independent variables are the key factors for obtaining good correlating and predicting models. No less important in modeling using ANNs is the relationship between the number of data and number of parameters to be determined, which depends on the number of layers and the number of neurons in each layer. An ANN usually has many more parameters than other statistical models, a fact that is an advantage and a disadvantage. Because many parameters need to be calculated (sometimes more that the data available), the problem becomes an optimization situation in which multiple optimum solutions exist. Usually the best model (set of parameters) calculated during training will be that giving good estimates during testing. That is the reason why when modeling using ANNs, a set of data must always be kept away for testing (and not used in training). In this way, the interpolating and predicting capabilities of the model can be tested. Usually the most appropriate number of layers and of neurons per layer is a matter of trial and error.6,7 It is not possible to tell beforehand what will be the best structure for a given application.
|% ΔTm| =
100 N
N
⎡ T cal − T lit ⎤ m m ⎥ Tmlit ⎦i ⎣
N
⎡ |T cal − T lit| ⎤ m m ⎥ Tmlit ⎦i ⎣
∑⎢ 1
(2)
Table 6. Deviations in Calculating Tm for 667 ILs (567 for Training and 100 for Testing) Using Different Architectures training (567 data)
testing (100 data)
architecture
% ΔTm
% |ΔTm|
% ΔTm
% |ΔTm|
(5, 5, 5, 1) (5, 10, 10, 1) (5, 15, 15, 1) (5, 20, 20, 1) (5, 25, 25, 1) (10, 5, 5, 1) (10, 10, 10, 1) (10, 15, 15, 1) (10, 20, 20, 1) (10, 25, 25, 1)
0.5 0.4 0.2 0.2 0.4 0.4 0.3 0.4 0.3 0.5
9.1 6.8 3.8 3.7 3.7 6.9 6.9 5.3 3.7 3.7
3.6 3.5 −0.9 0.6 0.2 0.9 0.9 −1.8 1.9 −1.1
15.7 16.4 15.2 14.6 14.9 14.9 14.8 13.5 15.7 14.6
results of these studies for 10 four-layer architectures, starting from a simple network of 16 neurons (5, 5, 5, 1) to a more complex network of 61 neurons (10, 25, 25, 1). As seen in Table 6, the results are variable, but the average deviations are relatively low (
